module Quox.Syntax.Term.Subst import Quox.No import Quox.Syntax.Term.Base import Quox.Syntax.Term.Tighten import Data.SnocVect %default total namespace CanDSubst public export interface CanDSubst (0 tm : TermLike) where (//) : tm dfrom n -> Lazy (DSubst dfrom dto) -> tm dto n ||| does the minimal reasonable work: ||| - deletes the closure around an atomic constant like `TYPE` ||| - deletes an identity substitution ||| - composes (lazily) with an existing top-level dim-closure ||| - otherwise, wraps in a new closure export CanDSubst Term where s // Shift SZ = s TYPE l loc // _ = TYPE l loc DCloT (Sub s ph) // th = DCloT $ Sub s $ ph . th s // th = DCloT $ Sub s th private subDArgs : Elim dfrom n -> DSubst dfrom dto -> Elim dto n subDArgs (DApp f d loc) th = DApp (subDArgs f th) (d // th) loc subDArgs e th = DCloE $ Sub e th ||| does the minimal reasonable work: ||| - deletes the closure around a term variable ||| - deletes an identity substitution ||| - composes (lazily) with an existing top-level dim-closure ||| - immediately looks up bound variables in a ||| top-level sequence of dimension applications ||| - otherwise, wraps in a new closure export CanDSubst Elim where e // Shift SZ = e F x u loc // _ = F x u loc B i loc // _ = B i loc e@(DApp {}) // th = subDArgs e th DCloE (Sub e ph) // th = DCloE $ Sub e $ ph . th e // th = DCloE $ Sub e th namespace DSubst.ScopeTermN export %inline (//) : ScopeTermN s dfrom n -> Lazy (DSubst dfrom dto) -> ScopeTermN s dto n S ns (Y body) // th = S ns $ Y $ body // th S ns (N body) // th = S ns $ N $ body // th namespace DSubst.DScopeTermN export %inline (//) : {s : Nat} -> DScopeTermN s dfrom n -> Lazy (DSubst dfrom dto) -> DScopeTermN s dto n S ns (Y body) // th = S ns $ Y $ body // pushN s th S ns (N body) // th = S ns $ N $ body // th export %inline FromVar (Elim d) where fromVarLoc = B export %inline FromVar (Term d) where fromVarLoc = E .: fromVar ||| does the minimal reasonable work: ||| - deletes the closure around a *free* name ||| - deletes an identity substitution ||| - composes (lazily) with an existing top-level closure ||| - immediately looks up a bound variable ||| - otherwise, wraps in a new closure export CanSubstSelf (Elim d) where F x u loc // _ = F x u loc B i loc // th = getLoc th i loc CloE (Sub e ph) // th = assert_total CloE $ Sub e $ ph . th e // th = case force th of Shift SZ => e th => CloE $ Sub e th namespace CanTSubst public export interface CanTSubst (0 tm : TermLike) where (//) : tm d from -> Lazy (TSubst d from to) -> tm d to ||| does the minimal reasonable work: ||| - deletes the closure around an atomic constant like `TYPE` ||| - deletes an identity substitution ||| - composes (lazily) with an existing top-level closure ||| - goes inside `E` in case it is a simple variable or something ||| - otherwise, wraps in a new closure export CanTSubst Term where TYPE l loc // _ = TYPE l loc E e // th = E $ e // th CloT (Sub s ph) // th = CloT $ Sub s $ ph . th s // th = case force th of Shift SZ => s th => CloT $ Sub s th namespace ScopeTermN export %inline (//) : {s : Nat} -> ScopeTermN s d from -> Lazy (TSubst d from to) -> ScopeTermN s d to S ns (Y body) // th = S ns $ Y $ body // pushN s th S ns (N body) // th = S ns $ N $ body // th namespace DScopeTermN export %inline (//) : {s : Nat} -> DScopeTermN s d from -> Lazy (TSubst d from to) -> DScopeTermN s d to S ns (Y body) // th = S ns $ Y $ body // map (// shift s) th S ns (N body) // th = S ns $ N $ body // th export %inline CanShift (Term d) where s // by = s // Shift by export %inline CanShift (Elim d) where e // by = e // Shift by export %inline {s : Nat} -> CanShift (ScopeTermN s d) where b // by = b // Shift by export %inline comp : DSubst dfrom dto -> TSubst dfrom from mid -> TSubst dto mid to -> TSubst dto from to comp th ps ph = map (// th) ps . ph public export %inline dweakT : (by : Nat) -> Term d n -> Term (by + d) n dweakT by t = t // shift by public export %inline dweakE : (by : Nat) -> Elim d n -> Elim (by + d) n dweakE by t = t // shift by public export %inline weakT : (by : Nat) -> Term d n -> Term d (by + n) weakT by t = t // shift by public export %inline weakE : (by : Nat) -> Elim d n -> Elim d (by + n) weakE by t = t // shift by parameters {s : Nat} namespace ScopeTermBody export %inline (.term) : ScopedBody s (Term d) n -> Term d (s + n) (Y b).term = b (N b).term = weakT s b namespace ScopeTermN export %inline (.term) : ScopeTermN s d n -> Term d (s + n) t.term = t.body.term namespace DScopeTermBody export %inline (.term) : ScopedBody s (\d => Term d n) d -> Term (s + d) n (Y b).term = b (N b).term = dweakT s b namespace DScopeTermN export %inline (.term) : DScopeTermN s d n -> Term (s + d) n t.term = t.body.term export %inline subN : ScopeTermN s d n -> SnocVect s (Elim d n) -> Term d n subN (S _ (Y body)) es = body // fromSnocVect es subN (S _ (N body)) _ = body export %inline sub1 : ScopeTerm d n -> Elim d n -> Term d n sub1 t e = subN t [< e] export %inline dsubN : DScopeTermN s d n -> SnocVect s (Dim d) -> Term d n dsubN (S _ (Y body)) ps = body // fromSnocVect ps dsubN (S _ (N body)) _ = body export %inline dsub1 : DScopeTerm d n -> Dim d -> Term d n dsub1 t p = dsubN t [< p] public export %inline (.zero) : DScopeTerm d n -> {default noLoc loc : Loc} -> Term d n body.zero = dsub1 body $ K Zero loc public export %inline (.one) : DScopeTerm d n -> {default noLoc loc : Loc} -> Term d n body.one = dsub1 body $ K One loc public export 0 CloTest : TermLike -> Type CloTest tm = forall d, n. tm d n -> Bool interface PushSubsts (0 tm : TermLike) (0 isClo : CloTest tm) | tm where pushSubstsWith : DSubst dfrom dto -> TSubst dto from to -> tm dfrom from -> Subset (tm dto to) (No . isClo) public export 0 NotClo : {isClo : CloTest tm} -> PushSubsts tm isClo => Pred (tm d n) NotClo = No . isClo public export 0 NonClo : (tm : TermLike) -> {isClo : CloTest tm} -> PushSubsts tm isClo => TermLike NonClo tm d n = Subset (tm d n) NotClo public export %inline nclo : {isClo : CloTest tm} -> (0 _ : PushSubsts tm isClo) => (t : tm d n) -> (0 nc : NotClo t) => NonClo tm d n nclo t = Element t nc parameters {0 isClo : CloTest tm} {auto _ : PushSubsts tm isClo} ||| if the input term has any top-level closures, push them under one layer of ||| syntax export %inline pushSubsts : tm d n -> NonClo tm d n pushSubsts s = pushSubstsWith id id s export %inline pushSubstsWith' : DSubst dfrom dto -> TSubst dto from to -> tm dfrom from -> tm dto to pushSubstsWith' th ph x = fst $ pushSubstsWith th ph x export %inline pushSubsts' : tm d n -> tm d n pushSubsts' s = fst $ pushSubsts s mutual public export isCloT : CloTest Term isCloT (CloT {}) = True isCloT (DCloT {}) = True isCloT (E e) = isCloE e isCloT _ = False public export isCloE : CloTest Elim isCloE (CloE {}) = True isCloE (DCloE {}) = True isCloE _ = False mutual export PushSubsts Term Subst.isCloT where pushSubstsWith th ph (TYPE l loc) = nclo $ TYPE l loc pushSubstsWith th ph (Pi qty a body loc) = nclo $ Pi qty (a // th // ph) (body // th // ph) loc pushSubstsWith th ph (Lam body loc) = nclo $ Lam (body // th // ph) loc pushSubstsWith th ph (Sig a b loc) = nclo $ Sig (a // th // ph) (b // th // ph) loc pushSubstsWith th ph (Pair s t loc) = nclo $ Pair (s // th // ph) (t // th // ph) loc pushSubstsWith th ph (Enum tags loc) = nclo $ Enum tags loc pushSubstsWith th ph (Tag tag loc) = nclo $ Tag tag loc pushSubstsWith th ph (Eq ty l r loc) = nclo $ Eq (ty // th // ph) (l // th // ph) (r // th // ph) loc pushSubstsWith th ph (DLam body loc) = nclo $ DLam (body // th // ph) loc pushSubstsWith _ _ (Nat loc) = nclo $ Nat loc pushSubstsWith _ _ (Zero loc) = nclo $ Zero loc pushSubstsWith th ph (Succ n loc) = nclo $ Succ (n // th // ph) loc pushSubstsWith th ph (BOX pi ty loc) = nclo $ BOX pi (ty // th // ph) loc pushSubstsWith th ph (Box val loc) = nclo $ Box (val // th // ph) loc pushSubstsWith th ph (E e) = let Element e nc = pushSubstsWith th ph e in nclo $ E e pushSubstsWith th ph (CloT (Sub s ps)) = pushSubstsWith th (comp th ps ph) s pushSubstsWith th ph (DCloT (Sub s ps)) = pushSubstsWith (ps . th) ph s export PushSubsts Elim Subst.isCloE where pushSubstsWith th ph (F x u loc) = nclo $ F x u loc pushSubstsWith th ph (B i loc) = let res = getLoc ph i loc in case nchoose $ isCloE res of Left yes => assert_total pushSubsts res Right no => Element res no pushSubstsWith th ph (App f s loc) = nclo $ App (f // th // ph) (s // th // ph) loc pushSubstsWith th ph (CasePair pi p r b loc) = nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph) loc pushSubstsWith th ph (CaseEnum pi t r arms loc) = nclo $ CaseEnum pi (t // th // ph) (r // th // ph) (map (\b => b // th // ph) arms) loc pushSubstsWith th ph (CaseNat pi pi' n r z s loc) = nclo $ CaseNat pi pi' (n // th // ph) (r // th // ph) (z // th // ph) (s // th // ph) loc pushSubstsWith th ph (CaseBox pi x r b loc) = nclo $ CaseBox pi (x // th // ph) (r // th // ph) (b // th // ph) loc pushSubstsWith th ph (DApp f d loc) = nclo $ DApp (f // th // ph) (d // th) loc pushSubstsWith th ph (Ann s a loc) = nclo $ Ann (s // th // ph) (a // th // ph) loc pushSubstsWith th ph (Coe ty p q val loc) = nclo $ Coe (ty // th // ph) (p // th) (q // th) (val // th // ph) loc pushSubstsWith th ph (Comp ty p q val r zero one loc) = nclo $ Comp (ty // th // ph) (p // th) (q // th) (val // th // ph) (r // th) (zero // th // ph) (one // th // ph) loc pushSubstsWith th ph (TypeCase ty ret arms def loc) = nclo $ TypeCase (ty // th // ph) (ret // th // ph) (map (\t => t // th // ph) arms) (def // th // ph) loc pushSubstsWith th ph (CloE (Sub e ps)) = pushSubstsWith th (comp th ps ph) e pushSubstsWith th ph (DCloE (Sub e ps)) = pushSubstsWith (ps . th) ph e private %inline CompHY : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) -> (r : Dim d) -> (zero, one : DScopeTerm d n) -> (loc : Loc) -> Elim d n CompHY {ty, p, q, val, r, zero, one, loc} = let ty' = SY ty.names $ ty.term // (B VZ ty.loc ::: shift 2) in Comp { ty = dsub1 ty q, p, q, val = E $ Coe ty p q val val.loc, r, -- [fixme] better locations for these vars? zero = SY zero.names $ E $ Coe ty' (B VZ zero.loc) (weakD 1 q) zero.term zero.loc, one = SY one.names $ E $ Coe ty' (B VZ one.loc) (weakD 1 q) one.term one.loc, loc } public export %inline CompH' : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) -> (r : Dim d) -> (zero : DScopeTerm d n) -> (one : DScopeTerm d n) -> (loc : Loc) -> Elim d n CompH' {ty, p, q, val, r, zero, one, loc} = case dsqueeze ty of S _ (N ty) => Comp {ty, p, q, val, r, zero, one, loc} S _ (Y _) => CompHY {ty, p, q, val, r, zero, one, loc} ||| heterogeneous composition, using Comp and Coe (and subst) ||| ||| comp [i ⇒ A] @p @q s @r { 0 j ⇒ t₀; 1 j ⇒ t₁ } ||| ≔ ||| comp [A‹q/i›] @p @q (coe [i ⇒ A] @p @q s) @r { ||| 0 j ⇒ coe [i ⇒ A] @j @q t₀; ||| 1 j ⇒ coe [i ⇒ A] @j @q t₁ ||| } public export %inline CompH : (i : BindName) -> (ty : Term (S d) n) -> (p, q : Dim d) -> (val : Term d n) -> (r : Dim d) -> (j0 : BindName) -> (zero : Term (S d) n) -> (j1 : BindName) -> (one : Term (S d) n) -> (loc : Loc) -> Elim d n CompH {i, ty, p, q, val, r, j0, zero, j1, one, loc} = CompH' {ty = SY [< i] ty, p, q, val, r, zero = SY [< j0] zero, one = SY [< j0] one, loc}